19O RECIPROCAL FIGURES, FRAMES, 



a finite portion of a surfece; in the second, it will correspond to several points, 

 HO that the lines, which correspond to the edges of such a polygon, will termi- 

 in several points, and not in one, as is necessary for reciprocity. 



Second Method of representing Stress in a Body. 



Let a, 6 be any two consecutive points in the first diagram, distant , 

 and o. /8 the corresponding points in the second, distant <r, then if the direc- 

 tion cosines of the line al are I, m, n and those of aft, X, p., v 



o-X = si -r- + &m -== + sn -p- 

 ax dy dz 



, dn (frj drj 



<ru. = sl -f^ + sm -j 1 +sn -j 1 



dx dy dz 



, d[ dl, dt, 



ov = 8l -j- + m T- + sn -s- 

 dx dy dz 



(12). 



Hence 



If we put l\ + mp. + nv = co&e, where e is the angle between s and o-, and if 

 we take three sets of values of I, m, n, corresponding to three directions at 

 right angles to each other, we find 



oj er, _ , <r, _ di- dy , d d*F , d*F , d*F 



Hence this quantity depends only on the position of the point, and not 

 on the directions of s u s u s t or of x, y, z, let us call it A'F. 



Now, let us take an element of area perpendicular to s, and let us sup- 

 pose that the stress on this element is compounded of a normal pressure = 



;md a tension parallel to <r and equal to p - . 



